• Previous Article
    A goethite process modeling method by Asynchronous Fuzzy Cognitive Network based on an improved constrained chicken swarm optimization algorithm
  • JIMO Home
  • This Issue
  • Next Article
    Side-information-induced reweighted sparse subspace clustering
May  2021, 17(3): 1253-1267. doi: 10.3934/jimo.2020020

Maximizing reliability of the capacity vector for multi-source multi-sink stochastic-flow networks subject to an assignment budget

Computer Science Branch, Mathematics Department, Faculty of Science, Aswan University, Aswan, Egypt

* Corresponding author: M. R. Hassan

Received  May 2019 Revised  August 2019 Published  May 2021 Early access  January 2020

Many real-world networks such as freight, power and long distance transportation networks are represented as multi-source multi-sink stochastic flow network. The objective is to transmit flow successfully between the source and the sink nodes. The reliability of the capacity vector of the assigned components is used an indicator to find the best flow strategy on the network. The Components Assignment Problem (CAP) deals with searching the optimal components to a given network subject to one or more constraints. The CAP in multi-source multi-sink stochastic flow networks with multiple commodities has not yet been discussed, so our paper investigates this scenario to maximize the reliability of the capacity vector subject to an assignment budget. The mathematical formulation of the problem is defined, and a proposed solution based on genetic algorithms is developed consisting of two steps. The first searches the set of components with the minimum cost and the second searches the flow vector of this set of components with maximum reliability. We apply the solution approach to three commonly used examples from the literature with two sets of available components to demonstrate its strong performance.

Citation: M. R. Hassan. Maximizing reliability of the capacity vector for multi-source multi-sink stochastic-flow networks subject to an assignment budget. Journal of Industrial and Management Optimization, 2021, 17 (3) : 1253-1267. doi: 10.3934/jimo.2020020
References:
[1]

A. AissouA. Daamouche and M. R. Hassan, Optimal components assignment problem for stochastic-flow networks, Journal of Computer Science, 15 (2019), 108-117. 

[2]

S. G. Chen, An optimal capacity assignment for the robust design problem in capacitated flow networks, Applied Mathematical Modelling, 36 (2012), 5272-5282.  doi: 10.1016/j.apm.2011.12.034.

[3]

S. G. Chen, Optimal double-resource assignment for the robust design problem in multistate computer networks, Applied Mathematical Modelling, 38 (2014), 263-277.  doi: 10.1016/j.apm.2013.06.020.

[4]

D. W. Coit and A. E. Smith, Penalty guided genetic search for reliability design optimization, Computers and Industrial Engineering, 30 (1996), 895-904. 

[5]

B. DengizF. Altiparmak and A. E. Smith, Local search genetic algorithm for optimal design of reliable networks, IEEE Transactions on Evolutionary Computation, 10 (1997), 179-188. 

[6]

M. Gen and R. Cheng, Genetic Algorithms and Engineering Optimization, 1$^{st}$ edition, Wiley Series in Engineering, Design, and Automation, 2000.

[7]

M. R. Hassan and H. Abdou, Multi-objective components assignment problem subject to lead-time constraints, Indian Journal of Science and Technology, 11 (2018), 1-9. 

[8]

M. R. Hassan, Solving a component assignment problem for a stochastic-flow network under lead-time constraint, Indian Journal of Science and Technology, 8 (2015), 1-5. 

[9]

M. R. Hassan, Solving flow allocation problems and optimizing system reliability of multisource multisink stochastic flow network, The International Arab Journal of Information Technology (IAJIT), 13 (2016), 477-483. 

[10]

C. C. Hsieh and Y. T. Chen, Reliable and economic resource allocation in an unreliable flow network, Computers and Operations Research, 32 (2005), 613-628. 

[11]

C. C. Hsieh and Y. T. Chen, Simple algorithms for updating multi-resource allocations in an unreliable flow network, Computers and Industrial Engineering, 50 (2006), 120-129. 

[12]

C. C. Hsieh and M. H. Lin, Reliability-oriented multi-resource allocation in a stochastic-flow network, Reliability Engineering and System Safety, 81 (2003), 155-161. 

[13]

Y.-K. Lin and C. T. Yeh, A two-stage approach for a multi-objective component assignment problem for a stochastic-flow network, Engineering Optimization, 45 (2013), 265-285.  doi: 10.1080/0305215X.2012.669381.

[14]

Y. K. Lin and C. T. Yeh, System reliability maximization for a computer network by finding the optimal two-class allocation subject to budget, Applied Soft Computing, 36 (2015), 578-588. 

[15]

Y. K. Lin and C. T. Yeh, Determining the optimal double-component assignment for a stochastic computer network, Omega, 40 (2012), 120-130. 

[16]

Y. K. Lin and C. T. Yeh, Evaluation of optimal network reliability under components-assignments subject to transmission budget, IEEE Transactions on Reliability, 59 (2010), 539-550. 

[17]

Y. K. Lin and C. T. Yeh, Maximal network reliability with optimal transmission line assignment for stochastic electric power networks via genetic algorithms, Applied Soft Computing, 11 (2011), 2714-2724. 

[18]

Y. K. Lin and C. T. Yeh, Multi-objective optimization for stochastic computer networks using NSGA-Ⅱ and TOPSIS, European Journal of Operational Research, 218 (2012), 735-746.  doi: 10.1016/j.ejor.2011.11.028.

[19]

Y. K. Lin and C. T. Yeh, Multistate components assignment problem with optimal network reliability subject to assignment budget, Applied Mathematics and Computation, 217 (2011), 10074-10086.  doi: 10.1016/j.amc.2011.05.001.

[20]

Y. K. Lin and C. T. Yeh, Optimal resource assignment to maximize multistate network reliability for a computer network, Computers and Operations Research, 37 (2010), 2229-2238.  doi: 10.1016/j.cor.2010.03.013.

[21]

Y. K. Lin and C. T. Yeh, Computer network reliability optimization under double-source assignments subject to transmission budget, Information Sciences, 181 (2011), 582-599. 

[22]

Y. K. LinC. T. Yeh and P. S. Huang, A hybrid ant-tabu algorithm for solving a multistate flow network reliability maximization problem, Applied Soft Computing, 13 (2013), 3529-3543. 

[23]

Q. LiuH. Z. Xiaoxian and Q. Zhao, Genetic algorithm-based study on flow allocation in a multicommodity stochastic-flow network with unreliable nodes, Eighth ACIS International Conference on Software Engineering, Artificial Intelligence, Networking, and Parallel/Distributed Computing, 8 (2007), 576-581. 

[24]

Q. LiuQ. Z. Zhao and W. K. Zang, Study on multi-objective optimization of flow allocation in a multi-commodity stochastic-flow network with unreliable nodes, Journal of Applied Mathematics Computing (JAMC), 28 (2008), 185-198.  doi: 10.1007/s12190-008-0093-9.

[25]

M. J. ZuoZ. Tian and H. Z. Huang, An efficient method for reliability evaluation of multistate networks given all minimal path vectors, IIE Transactions, 39 (2007), 811-817. 

show all references

References:
[1]

A. AissouA. Daamouche and M. R. Hassan, Optimal components assignment problem for stochastic-flow networks, Journal of Computer Science, 15 (2019), 108-117. 

[2]

S. G. Chen, An optimal capacity assignment for the robust design problem in capacitated flow networks, Applied Mathematical Modelling, 36 (2012), 5272-5282.  doi: 10.1016/j.apm.2011.12.034.

[3]

S. G. Chen, Optimal double-resource assignment for the robust design problem in multistate computer networks, Applied Mathematical Modelling, 38 (2014), 263-277.  doi: 10.1016/j.apm.2013.06.020.

[4]

D. W. Coit and A. E. Smith, Penalty guided genetic search for reliability design optimization, Computers and Industrial Engineering, 30 (1996), 895-904. 

[5]

B. DengizF. Altiparmak and A. E. Smith, Local search genetic algorithm for optimal design of reliable networks, IEEE Transactions on Evolutionary Computation, 10 (1997), 179-188. 

[6]

M. Gen and R. Cheng, Genetic Algorithms and Engineering Optimization, 1$^{st}$ edition, Wiley Series in Engineering, Design, and Automation, 2000.

[7]

M. R. Hassan and H. Abdou, Multi-objective components assignment problem subject to lead-time constraints, Indian Journal of Science and Technology, 11 (2018), 1-9. 

[8]

M. R. Hassan, Solving a component assignment problem for a stochastic-flow network under lead-time constraint, Indian Journal of Science and Technology, 8 (2015), 1-5. 

[9]

M. R. Hassan, Solving flow allocation problems and optimizing system reliability of multisource multisink stochastic flow network, The International Arab Journal of Information Technology (IAJIT), 13 (2016), 477-483. 

[10]

C. C. Hsieh and Y. T. Chen, Reliable and economic resource allocation in an unreliable flow network, Computers and Operations Research, 32 (2005), 613-628. 

[11]

C. C. Hsieh and Y. T. Chen, Simple algorithms for updating multi-resource allocations in an unreliable flow network, Computers and Industrial Engineering, 50 (2006), 120-129. 

[12]

C. C. Hsieh and M. H. Lin, Reliability-oriented multi-resource allocation in a stochastic-flow network, Reliability Engineering and System Safety, 81 (2003), 155-161. 

[13]

Y.-K. Lin and C. T. Yeh, A two-stage approach for a multi-objective component assignment problem for a stochastic-flow network, Engineering Optimization, 45 (2013), 265-285.  doi: 10.1080/0305215X.2012.669381.

[14]

Y. K. Lin and C. T. Yeh, System reliability maximization for a computer network by finding the optimal two-class allocation subject to budget, Applied Soft Computing, 36 (2015), 578-588. 

[15]

Y. K. Lin and C. T. Yeh, Determining the optimal double-component assignment for a stochastic computer network, Omega, 40 (2012), 120-130. 

[16]

Y. K. Lin and C. T. Yeh, Evaluation of optimal network reliability under components-assignments subject to transmission budget, IEEE Transactions on Reliability, 59 (2010), 539-550. 

[17]

Y. K. Lin and C. T. Yeh, Maximal network reliability with optimal transmission line assignment for stochastic electric power networks via genetic algorithms, Applied Soft Computing, 11 (2011), 2714-2724. 

[18]

Y. K. Lin and C. T. Yeh, Multi-objective optimization for stochastic computer networks using NSGA-Ⅱ and TOPSIS, European Journal of Operational Research, 218 (2012), 735-746.  doi: 10.1016/j.ejor.2011.11.028.

[19]

Y. K. Lin and C. T. Yeh, Multistate components assignment problem with optimal network reliability subject to assignment budget, Applied Mathematics and Computation, 217 (2011), 10074-10086.  doi: 10.1016/j.amc.2011.05.001.

[20]

Y. K. Lin and C. T. Yeh, Optimal resource assignment to maximize multistate network reliability for a computer network, Computers and Operations Research, 37 (2010), 2229-2238.  doi: 10.1016/j.cor.2010.03.013.

[21]

Y. K. Lin and C. T. Yeh, Computer network reliability optimization under double-source assignments subject to transmission budget, Information Sciences, 181 (2011), 582-599. 

[22]

Y. K. LinC. T. Yeh and P. S. Huang, A hybrid ant-tabu algorithm for solving a multistate flow network reliability maximization problem, Applied Soft Computing, 13 (2013), 3529-3543. 

[23]

Q. LiuH. Z. Xiaoxian and Q. Zhao, Genetic algorithm-based study on flow allocation in a multicommodity stochastic-flow network with unreliable nodes, Eighth ACIS International Conference on Software Engineering, Artificial Intelligence, Networking, and Parallel/Distributed Computing, 8 (2007), 576-581. 

[24]

Q. LiuQ. Z. Zhao and W. K. Zang, Study on multi-objective optimization of flow allocation in a multi-commodity stochastic-flow network with unreliable nodes, Journal of Applied Mathematics Computing (JAMC), 28 (2008), 185-198.  doi: 10.1007/s12190-008-0093-9.

[25]

M. J. ZuoZ. Tian and H. Z. Huang, An efficient method for reliability evaluation of multistate networks given all minimal path vectors, IIE Transactions, 39 (2007), 811-817. 

Figure 1.  Modified uniform crossover
Figure 2.  Mutation operation
Figure 3.  Crossover operation
Figure 4.  Mutation operation
Figure 5.  Network with three source and two sink nodes
Figure 6.  The minimum cost found at each generation
Figure 7.  Two-source two-sink computer network
Figure 8.  The minimum cost found at each generation
Figure 9.  Network with two source and three sink nodes
Figure 10.  The minimum cost found at each generation
Table 1.  Component information for the network in Figure 5
p Capacity Cost
0 1 2 3 4
1 0.02 0.04 0.14 0.80 0.00 1
2 0.04 0.06 0.10 0.15 0.65 3
3 0.02 0.03 0.05 0.90 0.00 4
4 0.05 0.08 0.87 0.00 0.00 2
5 0.01 0.04 0.10 0.85 0.00 3
6 0.02 0.05 0.15 0.78 0.00 2
7 0.05 0.10 0.85 0.00 0.00 1
8 0.04 0.06 0.15 0.75 0.00 4
9 0.03 0.05 0.12 0.80 0.00 1
10 0.01 0.04 0.05 0.15 0.75 3
11 0.03 0.05 0.07 0.85 0.00 1
12 0.01 0.02 0.07 0.90 0.00 1
p Capacity Cost
0 1 2 3 4
1 0.02 0.04 0.14 0.80 0.00 1
2 0.04 0.06 0.10 0.15 0.65 3
3 0.02 0.03 0.05 0.90 0.00 4
4 0.05 0.08 0.87 0.00 0.00 2
5 0.01 0.04 0.10 0.85 0.00 3
6 0.02 0.05 0.15 0.78 0.00 2
7 0.05 0.10 0.85 0.00 0.00 1
8 0.04 0.06 0.15 0.75 0.00 4
9 0.03 0.05 0.12 0.80 0.00 1
10 0.01 0.04 0.05 0.15 0.75 3
11 0.03 0.05 0.07 0.85 0.00 1
12 0.01 0.02 0.07 0.90 0.00 1
Table 2.  The initial population for the network example in Figure 5
No. The components$ \boldsymbol{(}\mathcal{B} $) The Flow vector (F) $ {\boldsymbol{Z}}_{\boldsymbol{obj}}\left(\mathcal{B}\right) $ $ \boldsymbol{R}\boldsymbol{(}{\boldsymbol{X}}_{\boldsymbol{F}}\boldsymbol{(}\mathcal{B}\boldsymbol{)} $
1 2 10 3 12 7 1 8 11 6 9 1 0 1 1 1 0 0 0 1 1 0 0 1 1 1 0 1 0 0 1 1 21.0067 0.259087
2 1 7 4 11 6 8 9 10 2 3 1 0 1 1 1 0 0 0 1 1 0 0 1 1 1 0 1 0 0 1 1 22.0005 0.288896
3 6 12 8 11 1 10 9 3 2 4 1 0 1 1 1 0 0 0 1 1 0 0 1 1 1 0 1 0 0 1 1 22.0164 0.236032
4 12 6 9 7 11 1 3 8 10 2 1 0 1 1 1 0 0 0 1 1 0 0 1 1 1 0 1 0 0 1 1 21.0002 0.293038
5 8 5 4 9 7 1 12 6 10 2 1 0 1 1 1 0 0 0 1 1 0 0 1 1 1 0 1 0 0 1 1 21.0036 0.269935
6 10 7 12 9 1 5 6 3 2 4 1 0 1 1 1 0 0 0 1 1 0 0 1 1 1 0 1 0 0 1 1 21.0002 0.292652
7 1 9 6 10 5 3 11 4 2 12 1 0 1 1 1 0 0 0 1 1 0 0 1 1 1 0 1 0 0 1 1 21.0000 0.312330
8 2 1 9 8 12 4 3 6 10 11 1 0 1 1 1 0 0 0 1 1 0 0 1 1 1 0 1 0 0 1 1 22.0012 0.282898
9 9 3 12 5 4 1 6 10 2 7 1 0 1 1 1 0 0 0 1 1 0 0 1 1 1 0 1 0 0 1 1 21.0002 0.293636
10 2 8 4 1 7 5 11 9 10 3 1 0 1 1 1 0 0 0 1 1 0 0 1 1 1 0 1 0 0 1 1 23.0000 0.314006
No. The components$ \boldsymbol{(}\mathcal{B} $) The Flow vector (F) $ {\boldsymbol{Z}}_{\boldsymbol{obj}}\left(\mathcal{B}\right) $ $ \boldsymbol{R}\boldsymbol{(}{\boldsymbol{X}}_{\boldsymbol{F}}\boldsymbol{(}\mathcal{B}\boldsymbol{)} $
1 2 10 3 12 7 1 8 11 6 9 1 0 1 1 1 0 0 0 1 1 0 0 1 1 1 0 1 0 0 1 1 21.0067 0.259087
2 1 7 4 11 6 8 9 10 2 3 1 0 1 1 1 0 0 0 1 1 0 0 1 1 1 0 1 0 0 1 1 22.0005 0.288896
3 6 12 8 11 1 10 9 3 2 4 1 0 1 1 1 0 0 0 1 1 0 0 1 1 1 0 1 0 0 1 1 22.0164 0.236032
4 12 6 9 7 11 1 3 8 10 2 1 0 1 1 1 0 0 0 1 1 0 0 1 1 1 0 1 0 0 1 1 21.0002 0.293038
5 8 5 4 9 7 1 12 6 10 2 1 0 1 1 1 0 0 0 1 1 0 0 1 1 1 0 1 0 0 1 1 21.0036 0.269935
6 10 7 12 9 1 5 6 3 2 4 1 0 1 1 1 0 0 0 1 1 0 0 1 1 1 0 1 0 0 1 1 21.0002 0.292652
7 1 9 6 10 5 3 11 4 2 12 1 0 1 1 1 0 0 0 1 1 0 0 1 1 1 0 1 0 0 1 1 21.0000 0.312330
8 2 1 9 8 12 4 3 6 10 11 1 0 1 1 1 0 0 0 1 1 0 0 1 1 1 0 1 0 0 1 1 22.0012 0.282898
9 9 3 12 5 4 1 6 10 2 7 1 0 1 1 1 0 0 0 1 1 0 0 1 1 1 0 1 0 0 1 1 21.0002 0.293636
10 2 8 4 1 7 5 11 9 10 3 1 0 1 1 1 0 0 0 1 1 0 0 1 1 1 0 1 0 0 1 1 23.0000 0.314006
Table 3.  The component information for the network of Figure 7.
p Capacity
0 1 2 3 4 5 6 7 8 9
1 0.001 0.001 0.003 0.004 0.005 0.005 0.006 0.007 0.010 0.015
2 0.001 0.003 0.003 0.004 0.005 0.007 0.007 0.008 0.009 0.010
3 0.002 0.002 0.003 0.006 0.007 0.007 0.010 0.012 0.015 0.017
4 0.001 0.001 0.002 0.003 0.005 0.008 0.010 0.011 0.012 0.015
5 0.001 0.002 0.009 0.012 0.020 0.040 0.050 0.060 0.806 0.000
6 0.001 0.002 0.002 0.005 0.010 0.012 0.015 0.017 0.020 0.025
7 0.001 0.001 0.002 0.005 0.008 0.010 0.012 0.015 0.015 0.017
8 0.001 0.002 0.005 0.005 0.007 0.008 0.010 0.012 0.015 0.015
9 0.001 0.001 0.002 0.002 0.003 0.004 0.005 0.008 0.009 0.010
10 0.002 0.003 0.005 0.006 0.007 0.009 0.012 0.015 0.941 0.000
11 0.002 0.002 0.003 0.005 0.007 0.008 0.010 0.011 0.020 0.030
12 0.001 0.002 0.003 0.005 0.008 0.009 0.010 0.012 0.015 0.040
13 0.001 0.001 0.003 0.005 0.005 0.010 0.011 0.017 0.018 0.020
14 0.001 0.001 0.002 0.002 0.003 0.005 0.007 0.009 0.016 0.021
15 0.001 0.001 0.002 0.003 0.004 0.005 0.007 0.008 0.009 0.011
16 0.001 0.002 0.002 0.004 0.005 0.006 0.007 0.009 0.014 0.017
17 0.001 0.001 0.002 0.002 0.003 0.004 0.005 0.007 0.009 0.011
18 0.001 0.001 0.002 0.002 0.002 0.003 0.003 0.004 0.005 0.007
19 0.001 0.001 0.002 0.003 0.005 0.008 0.009 0.011 0.013 0.014
20 0.002 0.002 0.003 0.006 0.007 0.007 0.010 0.013 0.015 0.020
10 11 12 13 14 15 16 17 18 19 20
0.060 0.150 0.733 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000
0.943 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000
0.919 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000
0.015 0.016 0.020 0.856 0.025 0.000 0.000 0.000 0.000 0.000 0.000
0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000
0.891 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000
0.020 0.022 0.025 0.030 0.817 0.000 0.000 0.000 0.000 0.000 0.000
0.016 0.020 0.884 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000
0.011 0.015 0.016 0.017 0.019 0.020 0.857 0.000 0.000 0.000 0.000
0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000
0.902 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000
0.895 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000
0.025 0.031 0.853 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000
0.024 0.025 0.030 0.035 0.040 0.060 0.719 0.000 0.000 0.000 0.000
0.015 0.017 0.020 0.027 0.870 0.000 0.000 0.000 0.000 0.000 0.000
0.020 0.022 0.025 0.030 0.035 0.040 0.761 0.000 0.000 0.000 0.000
0.015 0.017 0.018 0.019 0.020 0.022 0.844 0.017 0.017 0.000 0.000
0.008 0.009 0.011 0.013 0.014 0.014 0.015 0.000 0.000 0.019 0.020
0.015 0.017 0.020 0.030 0.851 0.000 0.000 0.000 0.000 0.000 0.000
0.915 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000
21 22 23 24 25 26 27 28 29 30 31
0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000
0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000
0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000
0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000
0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000
0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000
0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000
0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000
0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000
0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000
0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000
0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000
0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000
0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000
0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000
0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000
0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000
0.019 0.020 0.023 0.025 0.026 0.740 0.000 0.000 0.000 0.000 0.000
0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000
0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000
p Capacity
0 1 2 3 4 5 6 7 8 9
1 0.001 0.001 0.003 0.004 0.005 0.005 0.006 0.007 0.010 0.015
2 0.001 0.003 0.003 0.004 0.005 0.007 0.007 0.008 0.009 0.010
3 0.002 0.002 0.003 0.006 0.007 0.007 0.010 0.012 0.015 0.017
4 0.001 0.001 0.002 0.003 0.005 0.008 0.010 0.011 0.012 0.015
5 0.001 0.002 0.009 0.012 0.020 0.040 0.050 0.060 0.806 0.000
6 0.001 0.002 0.002 0.005 0.010 0.012 0.015 0.017 0.020 0.025
7 0.001 0.001 0.002 0.005 0.008 0.010 0.012 0.015 0.015 0.017
8 0.001 0.002 0.005 0.005 0.007 0.008 0.010 0.012 0.015 0.015
9 0.001 0.001 0.002 0.002 0.003 0.004 0.005 0.008 0.009 0.010
10 0.002 0.003 0.005 0.006 0.007 0.009 0.012 0.015 0.941 0.000
11 0.002 0.002 0.003 0.005 0.007 0.008 0.010 0.011 0.020 0.030
12 0.001 0.002 0.003 0.005 0.008 0.009 0.010 0.012 0.015 0.040
13 0.001 0.001 0.003 0.005 0.005 0.010 0.011 0.017 0.018 0.020
14 0.001 0.001 0.002 0.002 0.003 0.005 0.007 0.009 0.016 0.021
15 0.001 0.001 0.002 0.003 0.004 0.005 0.007 0.008 0.009 0.011
16 0.001 0.002 0.002 0.004 0.005 0.006 0.007 0.009 0.014 0.017
17 0.001 0.001 0.002 0.002 0.003 0.004 0.005 0.007 0.009 0.011
18 0.001 0.001 0.002 0.002 0.002 0.003 0.003 0.004 0.005 0.007
19 0.001 0.001 0.002 0.003 0.005 0.008 0.009 0.011 0.013 0.014
20 0.002 0.002 0.003 0.006 0.007 0.007 0.010 0.013 0.015 0.020
10 11 12 13 14 15 16 17 18 19 20
0.060 0.150 0.733 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000
0.943 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000
0.919 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000
0.015 0.016 0.020 0.856 0.025 0.000 0.000 0.000 0.000 0.000 0.000
0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000
0.891 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000
0.020 0.022 0.025 0.030 0.817 0.000 0.000 0.000 0.000 0.000 0.000
0.016 0.020 0.884 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000
0.011 0.015 0.016 0.017 0.019 0.020 0.857 0.000 0.000 0.000 0.000
0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000
0.902 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000
0.895 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000
0.025 0.031 0.853 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000
0.024 0.025 0.030 0.035 0.040 0.060 0.719 0.000 0.000 0.000 0.000
0.015 0.017 0.020 0.027 0.870 0.000 0.000 0.000 0.000 0.000 0.000
0.020 0.022 0.025 0.030 0.035 0.040 0.761 0.000 0.000 0.000 0.000
0.015 0.017 0.018 0.019 0.020 0.022 0.844 0.017 0.017 0.000 0.000
0.008 0.009 0.011 0.013 0.014 0.014 0.015 0.000 0.000 0.019 0.020
0.015 0.017 0.020 0.030 0.851 0.000 0.000 0.000 0.000 0.000 0.000
0.915 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000
21 22 23 24 25 26 27 28 29 30 31
0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000
0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000
0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000
0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000
0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000
0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000
0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000
0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000
0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000
0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000
0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000
0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000
0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000
0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000
0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000
0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000
0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000
0.019 0.020 0.023 0.025 0.026 0.740 0.000 0.000 0.000 0.000 0.000
0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000
0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000
[1]

Christopher Garcia. The synchronized multi-assignment orienteering problem. Journal of Industrial and Management Optimization, 2022  doi: 10.3934/jimo.2022018

[2]

Yi-Kuei Lin, Cheng-Ta Yeh. Reliability optimization of component assignment problem for a multistate network in terms of minimal cuts. Journal of Industrial and Management Optimization, 2011, 7 (1) : 211-227. doi: 10.3934/jimo.2011.7.211

[3]

Martin Gugat, Alexander Keimer, Günter Leugering, Zhiqiang Wang. Analysis of a system of nonlocal conservation laws for multi-commodity flow on networks. Networks and Heterogeneous Media, 2015, 10 (4) : 749-785. doi: 10.3934/nhm.2015.10.749

[4]

Peijun Li, Ganghua Yuan. Increasing stability for the inverse source scattering problem with multi-frequencies. Inverse Problems and Imaging, 2017, 11 (4) : 745-759. doi: 10.3934/ipi.2017035

[5]

Omer Faruk Yilmaz, Mehmet Bulent Durmusoglu. A performance comparison and evaluation of metaheuristics for a batch scheduling problem in a multi-hybrid cell manufacturing system with skilled workforce assignment. Journal of Industrial and Management Optimization, 2018, 14 (3) : 1219-1249. doi: 10.3934/jimo.2018007

[6]

Andrea Picco, Lamberto Rondoni. Boltzmann maps for networks of chemical reactions and the multi-stability problem. Networks and Heterogeneous Media, 2009, 4 (3) : 501-526. doi: 10.3934/nhm.2009.4.501

[7]

Loc H. Nguyen, Qitong Li, Michael V. Klibanov. A convergent numerical method for a multi-frequency inverse source problem in inhomogenous media. Inverse Problems and Imaging, 2019, 13 (5) : 1067-1094. doi: 10.3934/ipi.2019048

[8]

Jinsen Zhuang, Yan Zhou, Yonghui Xia. Synchronization analysis of drive-response multi-layer dynamical networks with additive couplings and stochastic perturbations. Discrete and Continuous Dynamical Systems - S, 2021, 14 (4) : 1607-1629. doi: 10.3934/dcdss.2020279

[9]

Haodong Chen, Hongchun Sun, Yiju Wang. A complementarity model and algorithm for direct multi-commodity flow supply chain network equilibrium problem. Journal of Industrial and Management Optimization, 2021, 17 (4) : 2217-2242. doi: 10.3934/jimo.2020066

[10]

Kien Ming Ng, Trung Hieu Tran. A parallel water flow algorithm with local search for solving the quadratic assignment problem. Journal of Industrial and Management Optimization, 2019, 15 (1) : 235-259. doi: 10.3934/jimo.2018041

[11]

Gunduz Caginalp, Mark DeSantis. Multi-group asset flow equations and stability. Discrete and Continuous Dynamical Systems - B, 2011, 16 (1) : 109-150. doi: 10.3934/dcdsb.2011.16.109

[12]

Zhiping Chen, Jia Liu, Gang Li. Time consistent policy of multi-period mean-variance problem in stochastic markets. Journal of Industrial and Management Optimization, 2016, 12 (1) : 229-249. doi: 10.3934/jimo.2016.12.229

[13]

Xiaoli Feng, Meixia Zhao, Peijun Li, Xu Wang. An inverse source problem for the stochastic wave equation. Inverse Problems and Imaging, 2022, 16 (2) : 397-415. doi: 10.3934/ipi.2021055

[14]

Alireza Eydi, Rozhin Saedi. A multi-objective decision-making model for supplier selection considering transport discounts and supplier capacity constraints. Journal of Industrial and Management Optimization, 2021, 17 (6) : 3581-3602. doi: 10.3934/jimo.2020134

[15]

Jinghuan Li, Shuhua Zhang, Yu Li. Modelling and computation of optimal multiple investment timing in multi-stage capacity expansion infrastructure projects. Journal of Industrial and Management Optimization, 2022, 18 (1) : 297-314. doi: 10.3934/jimo.2020154

[16]

Mahdi Karimi, Seyed Jafar Sadjadi. Optimization of a Multi-Item Inventory model for deteriorating items with capacity constraint using dynamic programming. Journal of Industrial and Management Optimization, 2022, 18 (2) : 1145-1160. doi: 10.3934/jimo.2021013

[17]

Massimiliano Caramia, Giovanni Storchi. Evaluating the effects of parking price and location in multi-modal transportation networks. Networks and Heterogeneous Media, 2006, 1 (3) : 441-465. doi: 10.3934/nhm.2006.1.441

[18]

Giulia Cavagnari, Antonio Marigonda, Benedetto Piccoli. Optimal synchronization problem for a multi-agent system. Networks and Heterogeneous Media, 2017, 12 (2) : 277-295. doi: 10.3934/nhm.2017012

[19]

Lihua Bian, Zhongfei Li, Haixiang Yao. Time-consistent strategy for a multi-period mean-variance asset-liability management problem with stochastic interest rate. Journal of Industrial and Management Optimization, 2021, 17 (3) : 1383-1410. doi: 10.3934/jimo.2020026

[20]

Emiliano Cristiani, Elisa Iacomini. An interface-free multi-scale multi-order model for traffic flow. Discrete and Continuous Dynamical Systems - B, 2019, 24 (11) : 6189-6207. doi: 10.3934/dcdsb.2019135

2020 Impact Factor: 1.801

Metrics

  • PDF downloads (287)
  • HTML views (678)
  • Cited by (1)

Other articles
by authors

[Back to Top]